315 research outputs found
Tangential Extremal Principles for Finite and Infinite Systems of Sets, II: Applications to Semi-infinite and Multiobjective Optimization
This paper contains selected applications of the new tangential extremal
principles and related results developed in Part I to calculus rules for
infinite intersections of sets and optimality conditions for problems of
semi-infinite programming and multiobjective optimization with countable
constraint
Variational Analysis in Semi-Infinite and Infinite Programming, II: Necessary Optimality Conditions
This paper concerns applications of advanced techniques of variational analysis and generalized differentiation to problems of semi-infinite and infinite programming with feasible solution sets defined by parameterized systems of infinitely many linear inequalities of the type intensively studied in the preceding development [5] from our viewpoint of robust Lipschitzian stability. We present meaningful interpretations and practical examples of such models. The main results establish necessary optimality conditions for a broad class of semi-infinite and infinite programs, where objectives are generally described by nonsmooth and nonconvex functions on Banach spaces and where infinite constraint inequality systems are indexed by arbitrary sets. The results obtained are new in both smooth and nonsmooth settings of semi-infinite and infinite programming
Approximate Optimality Conditions in Fractional Semi-Infinite Multiobjective Optimization (Study on Nonlinear Analysis and Convex Analysis)
This paper is based on the manuscript "Approximate necessary optimality in fractional semi-infinite multiobjective optimization" written by T. Shitkovskaya, Z. Hong, D.S. Kim and G.R. Piao, which was accepted to J. Nonlinear Convex Anal.This paper provides some new results on weak approximate solutions in fractional multiobjective optimization problems. Specifically, we establish necessary optimality conditions of Fritz-John type for a local weakly E-efficient solution in fuzzy form and, by using limiting constraint qualification, we provide necessary optimality conditions of Karush-Kuhn-Tucker type for a weakly E-quasi-efficient solution. To this purpose advanced tools of variational analysis and generalized differentiation are used
Optimality conditions in convex multiobjective SIP
The purpose of this paper is to characterize the weak efficient solutions, the efficient solutions, and the isolated efficient solutions of a given vector optimization problem with finitely many convex objective functions and infinitely many convex constraints. To do this, we introduce new and already known data qualifications (conditions involving the constraints and/or the objectives) in order to get optimality conditions which are expressed in terms of either Karusk–Kuhn–Tucker multipliers or a new gap function associated with the given problem.This research was partially cosponsored by the Ministry of Economy and Competitiveness (MINECO) of Spain, and by the European Regional Development Fund (ERDF) of the European Commission, Project MTM2014-59179-C2-1-P
On optimality conditions in nonsmooth semi-infinite vector optimization problems (Study on Nonlinear Analysis and Convex Analysis)
In this paper, we establish optimality conditions (both necessary and sufficient) for a nonsmooth semi-infinite vector optimization problem by using the scalarization method
Optimality Conditions for Nondifferentiable Multiobjective Semi-Infinite Programming Problems
We have considered a multiobjective semi-infinite programming problem with a feasible set defined by inequality constraints. First we studied a Fritz-John type necessary condition. Then, we introduced two constraint qualifications and derive the weak and strong Karush-Kuhn-Tucker (KKT in brief) types necessary conditions for an efficient solution of the considered problem. Finally an extension of a Caristi-Ferrara-Stefanescu result for the (Φ,ρ)-invexity is proved, and some sufficient conditions are presented under this weak assumption. All results are given in terms of Clark subdifferential
Robust optimality and duality for composite uncertain multiobjective optimization in Asplund spaces with its applications
This article is devoted to investigate a nonsmooth/nonconvex uncertain
multiobjective optimization problem with composition fields
((\hyperlink{CUP}{\mathrm{CUP}}) for brevity) over arbitrary Asplund spaces.
Employing some advanced techniques of variational analysis and generalized
differentiation, we establish necessary optimality conditions for weakly robust
efficient solutions of (\hyperlink{CUP}{\mathrm{CUP}}) in terms of the
limiting subdifferential. Sufficient conditions for the existence of (weakly)
robust efficient solutions to such a problem are also driven under the new
concept of pseudo-quasi convexity for composite functions. We formulate a
Mond-Weir-type robust dual problem to the primal problem
(\hyperlink{CUP}{\mathrm{CUP}}), and explore weak, strong, and converse
duality properties. In addition, the obtained results are applied to an
approximate uncertain multiobjective problem and a composite uncertain
multiobjective problem with linear operators.Comment: arXiv admin note: substantial text overlap with arXiv:2105.14366,
arXiv:2205.0114
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